Instead of using figs.savefig, try to use plt.savefig

import matplotlib.pyplot as plt
plt.savefig('static/images/staff_plot.png')

I guess you should import pyplot.

import matplotlib.pyplot as plt
plt.savefig()

I've adapted your code and took the liberty to change the several lines creating a figure by list in comprehension of for loops:

import matplotlib.pyplot as plt
# should be equal when using .pylab
import numpy.random as rnd

# generate_data
n_points = 1000
temperature_graph_array = rnd.random(n_points)
feelslike_graph_array = rnd.random(n_points)
windspeed_graph_array = rnd.random(n_points)
windgustspeed_graph_array = rnd.random(n_points)
pressure_graph_array = rnd.random(n_points)
humidity_graph_array = rnd.random(n_points)
list_of_data = [temperature_graph_array,
                feelslike_graph_array,
                windspeed_graph_array,
                windgustspeed_graph_array,
                pressure_graph_array,
                humidity_graph_array]
list_of_names = ['temperature',
                 'feelslike',
                 'windspeed',
                 'windgustspeed',
                 'pressure',
                 'humidity']

# create the figures:
#figure1 = plt.figure()
#figure2 = plt.figure()
#figure3 = plt.figure()
#figure4 = plt.figure()
#figure5 = plt.figure()
#figure6 = plt.figure()
#list_of_figs = [figure1, figure2, figure3, figure4, figure5, figure6]
## could be:
list_of_figs = [plt.figure() for i in range(6)]

# create the axis:
#ax1 = figure1.add_subplot(111)
#ax2 = figure2.add_subplot(111)
#ax3 = figure3.add_subplot(111)
#ax4 = figure4.add_subplot(111)
#ax5 = figure5.add_subplot(111)
#ax6 = figure6.add_subplot(111)
#list_of_axis = [ax1, ax2, ax3, ax4, ax5, ax6]
## could be:
list_of_axis = [fig.add_subplot(111) for fig in list_of_figs]

# plot the histograms
# notice `plt.hist` returns a tuple (n, bins, patches) or
# ([n0, n1, ...], bins, [patches0, patches1,...]) if the input
# contains multiple data
#hist1 = ax1.hist(temperature_graph_array, color="blue")
#hist2 = ax2.hist(feelslike_graph_array, color="blue")
#hist3 = ax3.hist(windspeed_graph_array, color="blue")
#hist4 = ax4.hist(windgustspeed_graph_array, color="blue")
#hist5 = ax5.hist(pressure_graph_array, color="blue")
#hist6 = ax6.hist(humidity_graph_array, color="blue")
#list_of_hists = [hist1, hist2, hist3, hist4, hist5, hist6]
## could be:
list_of_hists = []
for i, ax in enumerate(list_of_axis):
    list_of_hists.append(ax.hist(list_of_data[i], color="blue"))

filename = 'output_graph'
for i, fig in enumerate(list_of_figs):
    name = list_of_names[i].capitalize()
    list_of_axis[i].set_title(name)
    fig.tight_layout()
    fig.savefig("{}_{}.png".format(filename,name), format='png')

Will not post the resulting figures, but this gives me 6 little .png files in the same folder as the script.

Even better, you can use a function to do all that to your data:

def save_hist(data, name, filename):
    fig = plt.figure()
    ax = fig.add_subplot(111)
    ax.hist(data, color="blue")
    ax.set_title(name)
    fig.tight_layout()
    fig.savefig("{}_{}.png".format(filename,name), format='png')
    plt.close(fig)

filename = 'output_graph_2'
for data, name in zip(list_of_data, list_of_names):
    save_hist(data, name, filename)

Thanks for including the error, but what that's saying is that matplotlib doesn't have a savefig() function.

I think it's matplotlib.pyplot.savefig() as per this link: https://matplotlib.org/api/_as_gen/matplotlib.pyplot.savefig.html

Edit your code to say: plt.pyplot.savefig().

You can use ax.figure.savefig(), as suggested in a comment on the question:

import pandas as pd

df = pd.DataFrame([0, 1])
ax = df.plot.line()
ax.figure.savefig('demo-file.pdf')

This has no practical benefit over ax.get_figure().savefig() as suggested in other answers, so you can pick the option you find the most aesthetically pleasing. In fact, get_figure() simply returns self.figure:

# Source from snippet linked above
def get_figure(self):
    """Return the `.Figure` instance the artist belongs to."""
    return self.figure